Question

In: Math

We must show our work. 1. A sample of 81 observations is taken from a normal...

We must show our work.

1. A sample of 81 observations is taken from a normal population with a standard deviation of 5. The sample mean is 40. Determine the 80% confidence interval for the population mean. (Hint: Confidence Interval for a Population mean with population standard deviation (σ) known)

Solutions

Expert Solution

Solution :

Given that,

= 40

= 5

n = 81

At 80% confidence level the z is ,

  = 1 - 80% = 1 - 0.80 = 0.20

/ 2 = 0.20 / 2 = 0.10

Z/2 = Z0.10 = 1.28

Margin of error = E = Z/2* ( /n)

= 1.28 * (5 / 81)

= 0.71

At 80% confidence interval estimate of the population mean is,

- E < < + E

40 - 0.71 < < 40 + 0.71

39.29 < < 40.71

(39.29, 40.71)

milcah answered 1 year ago
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